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In the figure above, ED has a length of 4. What is the length of side

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In the figure above, ED has a length of 4. What is the length of side  [#permalink]

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New post 03 Nov 2018, 10:02
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In the figure above, ED has a length of 4. What is the length of side AC?
1) The perimeter of triangle EBD is 20.
2) Side AE = 8.

Weekly Quant Quiz #7 Question No 2


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Re: In the figure above, ED has a length of 4. What is the length of side  [#permalink]

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New post 03 Nov 2018, 10:12
In the figure above, ED has a length of 4. What is the length of side AC?
1) The perimeter of triangle EBD is 20.
2) Side AE = 8.

Perimeter of triangle EBD = ED + BE+BD = ED+2BE or ED+2*BD as angle BED and angle BDE are same
so BE = 8= BD\

angle BCA and angle BCA are equal hence AB = BC

But this is insufficient as if we draw a perpendicular from B on AC we need to know what AE is since AE + EP (lets say P is the point of perpendicular on AC) = PD+CD as perpendicular is the bisector in a isosceles triangle. (where 2 angles are equal)

So this is insufficient

2) AE= 8 is sufficient itself as we know EP which is half the ED since perpendicular is the bisector in isoscleles triangle

which is nothing but 2*(8+4/2)= 20

Hence B is sufficient
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Re: In the figure above, ED has a length of 4. What is the length of side  [#permalink]

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New post 03 Nov 2018, 10:15
1
In the figure above, ED has a length of 4. What is the length of side AC?
1) The perimeter of triangle EBD is 20.
2) Side AE = 8.


IN order to solve this question, we need to break down the question.
Angle DEB is the exterior angle to triangle ABC. Hence we can say that angle ABE=x

Hence, similarly Angle DBE is also x.

Traingle property: OPPOsite sides are equal.
We can infer: AE=BE
BD=DC
BD=BE

Hence AE=BE=BD=DC


Statement 1: Sufficent.
Since ED=4, BE=BD=8(20-4/2)
Which gives us a total value of 20 foe AC. (Inferred statements)

Statement 2: Sufficient.
Gives us AE=8
Hence Be=8=BD=Dc

Therefore AE+DE+Dc=20(8+4+8)


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Re: In the figure above, ED has a length of 4. What is the length of side  [#permalink]

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New post 03 Nov 2018, 10:23
Ans is b) alone 2nd is sufficient as in triangle BED ED=4
and if AE =8 so if we drop a perpendicular from b to ed at let say m then EM = 2
so now In triangle BAC AM=8+2=10
so AC = 10+10=20
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Re: In the figure above, ED has a length of 4. What is the length of side  [#permalink]

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New post 03 Nov 2018, 19:47
In the figure above, ED has a length of 4. What is the length of side AC?
1) The perimeter of triangle EBD is 20.
2) Side AE = 8.
_____________

Statement 1

Perimeter of EBD is 20 . Triangle EBD in an isosceles triangle. Hence

\(EB=BD=\frac{(Perimeter -ED)}{2}\)

=\(\frac{(20-4)}{2}\) =8

Also triangle ABE and Triangle BDC are congruent, Hence AE= CD

Also in Triangle AEB , \(Angle ABE =\frac{(180-2x-(180-4x))}{2}=\frac{2x}{2}=x\)
Hence AE=EB=8

Also as AE=CD

Hence, AC= AE+ED+CD= 8+4+8= 20 ( Hence, Statement 1 alone is sufficient)

Statement 2


AE=8

As triangle ABE and Triangle BDC are congruent, Hence AE= CD

Hence AC= AE+ED+CD= 8+4+8= 20 ( Hence, Statement 2 alone is also sufficient)

Hence the answer is D, Each statement alone is sufficient to answer the question


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Re: In the figure above, ED has a length of 4. What is the length of side  [#permalink]

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New post 04 Nov 2018, 01:48
In EBD , BE = BD and ED = 4

According to 1 , BE = 8
In ABE , BE = AE = 8
Same for BDC

According to 2 -> We are just working backwards for Statement 1

AC can found out through both individually so D
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Re: In the figure above, ED has a length of 4. What is the length of side   [#permalink] 04 Nov 2018, 01:48
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